The kidnapped seven-year-old daughter of a London-based management consultant was being reunited with her mother last night after police found her unharmed in an apartment in Baltimore, Maryland.

Police arrested the girl’s father, Clark Rockefeller, who had been posing as a member of the banking family.

Reigh Mills Boss, known as Snooks, became the focus of an international search after her father snatched her from a Boston street during a court-supervised custody visit last Sunday. After a series of reported sightings in America, Rockefeller was arrested after he left the apartment by himself.

“They got the girl,” a Boston police source told the Boston Herald newspaper. “She’s fine. He left her in the apartment.”

The girl’s mother is Sandra Boss, a high-flying American management consultant with McKinsey & Co who moved to London with Reigh after her divorce from Rockefeller last December.

Boss spent the week closeted in a hotel room in Boston waiting for news of her daughter, and was last night reported to be flying to Baltimore for a reunion with Reigh. It was not immediately clear how police tracked Rockefeller down. The 43-year-old father is expected to be charged with a variety of kidnapping-related charges in a court appearance tomorrow.

Earlier, US sources had indicated that Boss never knew the true identity of the man to whom she was married for 12 years. As part of her divorce agreement with Rockefeller, he was not required to produce a copy of his birth certificate or any other identification that might have explained when or why he changed his name.

The bizarre case of the high-flying businesswoman and the would-be Rockefeller had been tantalising Americans ever since it emerged that Reigh’s father had been lying about his past and had no connection with the Rockefeller oil and banking dynasty.

Police sources claimed that Rockefeller agreed to give up custody of Reigh last year in exchange for almost $1.5m from the sale of one of the couple’s former homes — and an agreement that he need not produce his birth certificate.

The custody deal allowed Boss to leave America with Reigh but was followed by a change of heart by Rockefeller, a stay-at-home father who had raised his daughter while her mother pursued her career. The missing pair were last seen at New York’s Grand Central station on Sunday.

It remains unclear how a brilliant businesswoman, with high society connections on both sides of the Atlantic, had come to be duped by such an improbable figure as Rockefeller. He had apparently long startled neighbours near the couple’s former country home with his eccentric behaviour and was said last week to have dyed his hair orange.

Apart from a brief public plea begging her former husband to “please, please, bring Snooks back”, Boss, who is said to earn £700,000 a year, has remained secluded in the Four Seasons hotel in Boston. Neither she nor any of her family or friends have been prepared to discuss the breakdown of the marriage, but police sources said the couple divorced in part over “identity issues”. Reigh’s last name was formally changed last year from Rockefeller to Mills Boss.

Mills is one of several aliases believed to have been adopted by Reigh’s father, who has turned out to have no longstanding government or work records in the name of Clark Rockefeller. It is not clear whether he admitted to his wife that Mills was his real name.

Police believe he may have concocted a fictional identity after studying the Rockefellers’ genealogy and finding a distant relative of the family named James Frederick Mills Clark, who is still alive and last week declared himself stunned that someone might have stolen parts of his name.

The couple were also said to have been at odds over Boss’s demanding job. As a managing partner in McKinsey’s Boston office, Boss was an expert on financial services and advised Michael Bloomberg, New York’s mayor, on maintaining his city’s competitiveness with London as a financial centre.

She was also a busy socialite who sat on the boards of several local foundations, notably as a trustee of the Mount, the former home of Edith Wharton, the 19th century novelist. “The mother was always working and Rockefeller essentially raised the child,” noted one Boston source. “But ultimately he refused to say who he was, and she got custody.”

Boss apparently never had a reason to suspect that the man she married was not a real Rockefeller. “He always seemed to have money,” a friend told the New York Post.

Where that money came from remains a mystery. Nobody called Clark Rockefeller has ever filed a tax return or held a bank account, credit card, passport or social security number, according to Boston police. Nor did Rockefeller have a driving licence; he was known among his neighbours for not being able to drive and was often seen buzzing around on a Segway electric transporter.

Over the years he told many tales about his life, variously claiming to be a mathematician, a physicist, an economics adviser to developing countries, and that he was working secretly for the Pentagon. He also claimed to have inherited a fortune from parents who died in a Connecticut car crash, but police have found no evidence of their existence.

Secret lives

Clark Rockefeller seems to be the latest in a long line of people who have masked their identity to evade detection.

Charles Stopford, a former US serviceman, fled to England and assumed the name Christopher Buckingham in 1983 by stealing the identity of a dead baby. He married, had two children and later posed as an earl. His family did not discover his secret until 2005 when he was stopped by immigration officials at Calais.

Andreas Grassl, 20, turned up on a Kent beach in 2005 suffering apparent memory loss. He became known as the Piano Man after playing music but refusing to speak. It later turned out that he had fled Germany after a breakdown.

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